Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. x^2≥0

Verified step by step guidance

1. Step 1: Recognize that the inequality $x^2\ge 0$ is asking for all values of $x$ where the square of $x$ is greater than or equal to zero.
2. Step 2: Understand that any real number squared is always non-negative, meaning $x^2\ge 0$ is true for all real numbers.
3. Step 3: Conclude that the solution set for $x^2\ge 0$ includes all real numbers.
4. Step 4: Express the solution set in interval notation. Since all real numbers satisfy the inequality, the interval is $(-\mathrm{\infty },\mathrm{\infty })$.
5. Step 5: Match this interval notation with the corresponding option in Column II.

Key Concepts

Inequalities

Inequalities express a relationship between two expressions that are not necessarily equal. In this case, the inequality x^2 ≥ 0 indicates that the square of x is greater than or equal to zero. Understanding how to manipulate and interpret inequalities is crucial for solving problems that involve ranges of values.

Interval Notation

Interval notation is a mathematical notation used to represent a set of numbers between two endpoints. It uses brackets [ ] to include endpoints and parentheses ( ) to exclude them. For the inequality x^2 ≥ 0, the equivalent interval notation would be (-∞, ∞), as all real numbers satisfy this condition.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form f(x) = ax^2 + bx + c. The graph of a quadratic function is a parabola, and its properties, such as the vertex and axis of symmetry, help in analyzing inequalities like x^2 ≥ 0. Since the square of any real number is non-negative, this function is always above or on the x-axis.